5. Application examples

There are many practical applications of structured or unstructured kinetic models. In the acetone-butanol-ethanol (ABE) production, the models for the bioprocess have evolved from simple stoichiometric equations to sophisticated and elaborate kinetic models based on metabolic pathways [33, 34], genome-scale metabolic flux modeling [35], system-level modeling [34], and metabolic network [21]. Gordeeva classified mathematical modeling of specific growth rate (dependent or independent on substrate concentration), specific rate of substrate consumption, and specific rate of product formation in batch fermentations [36]. In this study, the states in fermentation are described by a system of three ODEs [36]. Cui reported unstructured lactate formation by enzymatic hydrolysis of sugarcane bagasse, and the model is based on Logistic equations, Luedeking-Piret equations and Luedeking-Piret-like equations [37]. Similarly, Sharma reported an unstructured model to describe growth, substrate utilization, and lactate production by Lactobacillus plantarum [38]. On the other hand, the common mathematical descriptions of the fermentation process are based on UKMs. For example, the fermentation of sweet sorghum stalk juice by immobilized Saccharomyces cerevisiae is explained by the kinetic parameters of Hinshelwood's model [39]. Another example using the UKM

Fermentation: Metabolism, Kinetic Models, and Bioprocessing DOI: http://dx.doi.org/10.5772/intechopen.82195

In bioreactor design, soft sensors can be used to estimate unavailable variables such as biomass. Traditionally, biomass has been traditionally determined by use of a variety of methodologies such as optical density, dry weight, and microbial counts, among others. These techniques present several problems, the most important being the lack of continuous online measurements. To overcome this problem, various strategies have been applied, such as the implementation of low-cost sensors combined with signal processing strategies. For instance, the RGB sensor is used for biomass measurement in microalgae production reactors [29]. This type of sensors uses the intensity of the red, green, and blue (RGB) colors, which correlates with the biomass concentration using dry weight and/or colony formation unit (CFU) information, using the Beer-Lambert law principles. The correlation is described through linear fitting [30]. Additionally, it is possible to compensate background noise by use of ANNs even in the case of nonlinear correlation [31]. Soft sensors can also be applied to nonexplicit system states. These observers can

estimate lumped system variables, such as growth rate. As the simplest factor, temperature is commonly used, since it allows estimating system concentrations, due to intrinsic dependence between reaction rates and reaction enthalpy. The heat of reaction, either consumed or dissipated by the system, is one of the implicit system states used for reaction rate determination. The same strategy may also be

Microbial growth rates are inherently variable due to their metabolic nature and operation conditions. For example, as fluctuation in substrate concentration occurs in fed-batch bioreactors, the condition of osmotic pressure within cells is modified through the plasma membrane, which may change cellular energetics and the viability of cell division. A suitable strategy for these cases is the design of a substrate consumption rate observer. This kind of observer helps to design a robust control strategy against important fluctuations in maintaining constant substrate

The use of observers or soft sensors is an interesting alternative to elucidate approximate values of system states, whether these are explicit or implicit, in cases where online continuous physical measurement is not available. These approximations can be used to design process control schemes that ensure proper functioning.

There are many practical applications of structured or unstructured kinetic models. In the acetone-butanol-ethanol (ABE) production, the models for the bioprocess have evolved from simple stoichiometric equations to sophisticated and elaborate kinetic models based on metabolic pathways [33, 34], genome-scale metabolic flux modeling [35], system-level modeling [34], and metabolic network [21]. Gordeeva classified mathematical modeling of specific growth rate (dependent or independent on substrate concentration), specific rate of substrate consumption, and specific rate of product formation in batch fermentations [36]. In this study, the states in fermentation are described by a system of three ODEs [36]. Cui reported unstructured lactate formation by enzymatic hydrolysis of sugarcane bagasse, and the model is based on Logistic equations, Luedeking-Piret equations and Luedeking-Piret-like equations [37]. Similarly, Sharma reported an unstructured model to describe growth, substrate utilization, and lactate production by Lactobacillus plantarum [38]. On the other hand, the common mathematical descriptions of the fermentation process are based on UKMs. For example, the fermentation of sweet sorghum stalk juice by immobilized Saccharomyces cerevisiae is explained by the kinetic parameters of Hinshelwood's model [39]. Another example using the UKM

used to determine microbial growth rates [32].

Current Topics in Biochemical Engineering

concentrations.

20

5. Application examples

model is the basic logistic model incorporated with the Luedeking-Piret model (hybrid model) to describe the production of bioethanol from banana and pineapple wastes [40].

Cephalosporium acremonium (ATCC 36225) is one example of the utilization of SKMs where morphological differentiation and catabolite repression are the main aspects of the model approach [41]. SKMs can also effectively represent diauxic growth as well as the monitoring of an intracellular reactant in acetic acid production by Bacillus licheniformis [42]. Sansonetti reported a biochemically structured model for ethanol production from ricotta cheese whey by Kluyveromyces marxianus [43]. Wang studied a segregated kinetic model in fed-batch culture to represent simultaneous saccharification and co-fermentation (SSCF) for bioethanol production from lignocellulosic raw materials at high substrate concentrations [44]. Another interesting process is the solid-state fermentation. In most proposed models, a set of PDEs is used to describe how intraparticles are diffused or how the growth can be affected by intraparticle diffusion of oxygen, enzymes, hydrolysis products, and other nutrients and the role in the fermentation of other phenomena such as particle shrinkage and spatial microbial biomass distribution [45]. Computational fluid dynamics (CFD) provides information concerning the mixing modeling and design of bioreactors [46]. Another example of CFD is cephalosporin production by Acremonium chrysogenum; it was found that the oxygen transfer rate (OTR) directly affects fermentation performance with different impeller combinations [47]. Applications of CFD to fermentation modeling include effects of stress on cell morphology and mass transfer from the bulk solution to the organisms [46]. Biochemical models should be coupled to the CFD models in order to give a closed link between biochemistry and fluid dynamics of the system [33]. Haringa assesses the effect of substrate heterogeneity on the metabolic response of P. chrysogenum in industrial bioreactors via coupling of a 9-pool metabolic model with Euler-Lagrange CFD simulations toward rational scale-down and design optimization [48].

Another way to construct mathematical models of microbial growth is the use of FFNs, which describe the behavior of different configurations of bioreactors. An example of this type of applications is the modeling of the production of bioethanol obtained from sugar beets [49]. Here, a three-layer FFN is used to describe the dynamic behavior of the reactor. The first neuron layer consists of system inputs, which correspond to substrate concentration, substrate type, and fermentation time. The second layer corresponds to hidden neurons that process the information through their activation function. Finally, the third layer matches the output of the system that corresponds to the viable cell count of yeasts and the concentration of ethanol produced. On the other hand, GBMs and their hybrid models are not only used to characterize fermentation kinetics but can also describe general behaviors of bioprocesses. For example, in fed batch cultures of Chlorella pyrenoidosa, a hybrid scheme of ANN with mass balance mechanistic models describes the general behavior of the states of the system, reducing considerably the variability of their predictions, and achieving versatility in application [50]. These types of GBMs are useful in cases of high complexity due to metabolic dynamics of microorganisms [51]. GBMs or hybrid models are not only combinations of first principles with ANNs, but there may also be hybrid models obtained through the combination of statistical models with ANNs. This type of models usually has special applicability in the optimization of operating conditions of bioreactors (e.g., fed batch fermentation of Ralstonia eutropha for poly-βhydroxybutyrate production) [52].

Soft sensors are also useful in control design. For example, sliding mode observers can describe the behavior of sulfate reduction rate which results from Desulfovibrio alaskensis fermentation [53]. These observers use turbidimetric and colorimetric titration information, and formulate based on sliding modes and sigmoidal functions, but their performance depends strongly on the nature of the system and its monitoring schemes.

Abrupt leaps in substrate concentration can be detected and prevented by the strategy of adaptive or optimal control by coupling with an observation scheme such as ANNs. For example, in L-glutamate production with Corynebacterium glutamicum fermentation, physical sensor applications are limited because of high costs and system complexity. However, it is possible to use simpler measurements such as oxygen concentrations, temperature, pH, and carbon dioxide production to train models of ANNs that can approximate the dynamic behavior of glucose concentration [54].
